Chain Dimensions and Entanglement Spacings

Abstract

This chapter summarizes data on chain dimensions and entanglement spacings for a number of linear flexible polymers. While polymer chain entanglement is far from being understood, one natural idea based on overlap appears useful for thinking about entanglement effects in polymer melts. This concept leads to the entanglement criterion: a fixed number of entanglement strands (Pe) share a volume equal to the cube of the tube diameter (a3). One of the main purposes of this chapter is to test this criterion using literature data on flexible polymer melts and evaluate this universal number. Empirical relations useful for estimating plateau modulus and entanglement molar mass of polymer melts emerge from this analysis. Chain entanglement is important, not merely for melt rheology, but also for mechanical properties of glassy and semicrystalline polymers. This chapter first discusses chain dimensions of polymers and then discusses chain entanglement and the tube diameter. The critical molar mass for entanglement effects in melt viscosity is then discussed, followed by the temperature dependence of chain dimensions. Molecular characteristics of various polymers and coploymers are tabulated. Entanglement and critical molecular weights of various polymers are tabulated.